Gaffney suffered the injury on his first play of Friday night's practice at Bank of America Stadium in Charlotte, North Carolina. He showed up at Wofford's Gibb's Stadium on Saturday night on crutches and in street clothes.
His injury, along with Jonathan Stewart being out indefinitely with a hamstring injury suffered a week and a half ago while conditioning in California, leaves the Panthers thin at running back.
Coach Ron Rivera said the team will sign another back to fill Gaffney's roster spot.
"It's disappointing because the young man is a solid football player," Rivera said. "He has a history of being a workhorse. Unfortunately, in practice he got his knee in a bad position and something popped."
Gaffney had 330 carries for 1,709 yards last season at Stanford. In 486 carries in college he never had an injury.
"It was on a running play," Rivera said. "He ran a sweep coming out to our offensive left [side]. He made a really nice cut. It was a bump and a little bit of a turn on the knee and he said he felt it pop."
The Panthers are down to DeAngelo Williams, Mike Tolbert and Kenjon Barner as they head into Sunday's first practice in pads. Stewart said earlier in the day his hamstring injury wasn't serious, but he could be out two to four weeks.
"We are a little bit thin," Rivera said. "We're going to find somebody to come in and replace him and give him an opportunity to have another body to compete for a position on this team."